The invention concerns a calibration method for an MPI apparatus to perform an MPI experiment, wherein the calibration method comprises M calibration MPI measurements with a calibration sample and uses these measurements to create an image reconstruction matrix with which the signal contributions of N voxels within a volume under investigation of the MPI apparatus are determined.
A method of this type is disclosed e.g. by references [WGR09] or [KSB10].
Magnetic particle imaging (abbreviation “MPI”) is a new imaging method that allows to determine the spatial distribution of magnetic nanoparticles [WGR09]. For this purpose, the particles are exposed to different static and dynamic magnetic fields and the changes in magnetization of the particles are detected using receiver coils. MPI utilizes a magnetic gradient field that has a field-free point (FFP) for spatial encoding. Shifting the FFP along a pre-defined trajectory allows scanning of the measurement range to be investigated, thereby using dynamic excitation fields (drive fields).
The correlation between the particle distribution to be reconstructed c(r) and the spectral coefficients of the measuring signal ûk k=0, . . . , K−1 can be described by a linear integral equation
                                          u            ^                    k                =                              ∫            Object                    ⁢                                    c              ⁡                              (                r                )                                      ⁢                                          s                k                            ⁡                              (                r                )                                      ⁢                          d              3                        ⁢            r                                              (        1        )            
sk(r) thereby describes the system function which depends both on the location r and also on the frequency index k. The number of available frequencies K depends on the time resolution of the measurement hardware and on the utilized measurement trajectory.
There are different methods for determining the system function, which are either based on a model of the MPI signal chain or on a calibration measurement. In the standard method used up to now, a small sample filled with particles (calibration sample) in the form of an image voxel is used. When the sample is positioned at a position r′ and a measurement ûk′ is subsequently recorded using the MPI system, the system function at this location can be approximated by
                                          s            k                    ⁡                      (                          r              ′                        )                          ≈                                            u              ^                        k            ′                                              V              0                        ⁢                          c              0                                                          (        2        )            
V0 designates the volume and c0 designates the particle concentration of the calibration sample. The smaller the calibration sample the better the approximation. Recording of the system function at all positions in the measurement range requires movement of the calibration sample by means of a positioning robot. The calibration sample is thereby alternately moved to the subsequent position followed by measurement recording using the MPI system. Normally a Cartesian grid with spatial points rn, n=0, . . . , N−1 is used. N thereby designates the overall number of scanning points.
After discretization of the equation system (1) at points rn, n=0, . . . , N−1, one obtains a linear equation systemû=Sc,  (3)which is to be solved in order to reconstruct the MPI measurement data. During calibration measurement, the system matrix is measured in columns. The n-th calibration measurement is multiplied by a factor of 1/(V0 c0) and entered in the n-th column of the system matrix.
The above described method for determining the system function is advantageous in that it can determine the actual physical processes during an MPI experiment. This method, however, is disadvantageous in that certain parts of the system function determined in this fashion may be noisy, since an MPI measurement basically contains noise. One even more substantial disadvantage, however, is the time expenditure of the method. In [WGR09], the determination of a 3D system function on a coarse grid of a size of 34×20×28, which covers a measuring field of 20.4×12×16.8 mm3, required approximately 6 hours. On a finer grid, the determination of the system function would require days to months, which is not applicable in practice.
[KSB10] discloses an alternative method. This method utilizes a model of the MPI signal chain instead of a complex calibration measurement. The method is much faster, but is disadvantageous, since it does not achieve the accuracy of the measured system function, which is mainly due to the fact that up to now, nobody has found a particle model that describes the physical behavior of the particles with sufficiently precision.
It is not necessary for the size of the calibration sample and the size of an image voxel to coincide. It may e.g. be reasonable to use a larger calibration sample in order to improve the signal-to-noise ratio of the measurement data, which might, however, be accompanied by a loss in resolution. [HBRGB12] discloses a calibration method, in which the mechanical motion of the point sample is replaced by electromagnetic motion of the magnetic fields. For this purpose, the calibration sample is positioned at a fixed location. Subsequently, the same static magnetic field that prevails at the voxel positions in the measuring field to be measured, is successively generated at the location of the calibration sample. This accelerates the calibration measurement, since an electromagnetic field change can be realized more quickly than mechanical movement of the calibration sample. The method proposed in this invention does not depend on whether the calibration data is recorded by mechanical or electromagnetic steps.
While in [WGR09] the overall measuring volume is covered by the measurement trajectory, in case of larger MPI scanners (e.g. for applications on human beings) only a small area of the overall measuring volume (patient volume) may be covered by varying the excitation field. In this case, a multi-station approach can be used, in which small subvolumes are successively scanned. In this case, a dedicated system matrix must be recorded for each subvolume. The method proposed in this invention can be applied for any subvolume in this case.
Departing therefrom, it is the underlying purpose of the present invention to specify a more efficient method for determining the system matrix for the imaging MPI method, which determines an MPI system function within a short time, thereby nevertheless achieving high accuracy.